In this paper we study some new theories of characteristic homology classes of singular
complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class …

The notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced,
and the relation between them is studied. The elliptic genus of singular varieties is given in …

Based on recent advances on the relation between geometry and representation theory, we
propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic …

In this survey paper we review recent advances in the calculus of Chern-Schwartz-
MacPherson, motivic Chern, and elliptic classes of classical Schubert varieties. These three …

We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov–Libgober
classes of Schubert varieties in general homogeneous spaces G/P. While these classes do …

We prove functorial weak factorization of projective birational morphisms of regular
quasiexcellent schemes in characteristic 0 broadly based on the existing line of proof for …

We survey the push-forward formula for elliptic class and various applications obtained in
the papers by L. Borisov and the author. We then discuss the ring of quasi-Jacobi forms …

We determine the possible finite groups $ G $ of symplectic automorphisms of hyperk\" ahler
manifolds which are deformation equivalent to the second Hilbert scheme of a K3 surface …

The theory of characteristic classes of vector bundles and smooth manifolds plays an
important role in the theory of smooth manifolds. An investigation of reasonable notions of …

Characteristic classes of Schubert varieties can be used to study the geometry and the
combinatorics of homogeneous spaces. We prove a relation between elliptic classes of …